http://imagej.273.s1.nabble.com/FFT-Filtering-are-non-symmetric-masks-useful-tp3697755p3697761.html
> Michael, Albert, and Joachim,
>
> Maybe something in the link below will help. As I recall, the .doc
> and the .ppt both present the conversions. When the FHT was
> invented there was a lot of discussion about its pros and cons vs.
> the FFT, but I think the current understanding is that there is no
> important difference.
>
http://imagejdocu.tudor.lu/Members/ajahnen/
> conference_proceedings_2006/Robert%20Dougherty
>
> Bob
>
> On Dec 13, 2007, at 9:53 AM, Joachim Wesner wrote:
>
>> Hi Michael, Hi others,
>>
>> as I´m unfortunatelly busy with preparing a company presentation
>> till next
>> monday I cannot look further into this
>> issue instantelly (even if I would like to), but plan to attack it
>> next
>> week
>>
>> Actually, FHT vs. FFT is only another way of rearranging the
>> complex result
>> of a real to complex FFT
>> and somehow redefining what "negative" frequencies mean. The
>> complex FFT
>> extension I did basically does
>> 2 FHTs and unscrambles the result so that it should be equivalent
>> to a real
>> complex FFT. I.e. in most cases
>> the difference *should* be only in the relative order of 1e-6
>> (rounding
>> errors) or so. (IIRC the "trick" is to calculate
>> the sum and difference of negative and positive "FHT frequencies"
>> to get
>> what would be the FFT real and imag part.)
>>
>> However I have to admit that I personally regularly only use a
>> plugin of
>> mine that has these extensions as a private copy
>> and does not rely on the IJ built in version (even if I did
>> thorough(?)
>> testing before Wayne added the code), so I can
>> in the moment not say what the recent status of the bult in
>> version is. Yet
>> I´m quite confident that the above mentioned
>> "unscrambling" principle works as should be and does indeed give
>> results in
>> agreement with a true FFT within about 1e-6
>> as it should be, used it a lot.
>>
>> I will play around with your macros and others to test. More soon!
>>
>> "Sorry for any inconvenience" ;-))
>>
>> Mit freundlichen Grüßen / Best regards
>>
>> Joachim Wesner
>> Projektleiter Optik Technologiesysteme
>>
>> Ernst Leitz Strasse 17-37 | 35578 Wetzlar (Germany)
>> Tel. +49 6441 29 2611 | Fax +49 6441 29 2700
>>
>> ____________________________________________
>>
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>>
>>
>> Michael Schmid
>> <
[hidden email]
>>
>> N.AC.AT> An
>> Gesendet von:
[hidden email]
>> ImageJ
>> Interest Kopie
>> Group
>>
>> <
[hidden email]. Thema
>> GOV> Re: Antwort: FFT-Filtering
>> - are
>> non-symmetric masks useful?
>>
>> 13.12.2007 14:20
>>
>>
>> Bitte antworten
>> an
>> ImageJ Interest
>> Group
>> <
[hidden email].
>> GOV>
>>
>>
>>
>>
>>
>>
>> Hi Albert,
>>
>> maybe you are right that the problem is the FHT (Hartley
>> transform), but I think that one should be able to get the FFT
>> coefficients from an FHT.
>> Anyhow, it seems to me that this does not work as expected.
>>
>> For example, the power spectrum of a sum of two sine or
>> cosine functions with different amplitudes looks like the
>> square of a power spectrum to me. Twice the amplitude gives
>> 16 times the intensity in the power spectrum, not 4 times as I
>> would expect.
>> (I used the "raw" power spectrum, not the log-scaled one)
>>
>> Below is the macro that I use for testing - it creates a sum of
>> one-dimensional sin and cos functions.
>>
>> Further, in the "Complex FFT", a sin(x) function does not give
>> an imaginary result as I would have expected.
>> Strange enough, when trying a simple sinusoidal function with
>> different phaseshifts, I always get a real result (apart from
>> numeric noise in the imaginary channel).
>>
>> One more point, but this could be resolved more easily:
>> With FFT Math>Correlate, when correlating an image with itself
>> and doing no inverse transformation I would expect to get the
>> unscaled power spectrum, not the log-scaled one.
>>
>> Below is the macro that I use for testing - it creates a
>> one-dimensional sin and cos function.
>>
>> Maybe Joachim Wesner, the FFT/FHT expert in the group, can say
>> more about this, whether it is a limitation inherent to the
>> FHT or some more mundane problem?
>>
>>
>> Michael
>> ________________________________________________________________
>> // T E S T M A C R O
>> newImage("test", "32-bit Black", 256, 256, 1);
>> pi = 3.1415926536;
>> f1 = 1*2*pi/256;
>> f2 = 2*2*pi/256;
>>
>> for (x=0; x<255; x++) {
>> //v = sin(f1*x + pi/8);
>> v = sin(f1*x)+0.5*cos(f2*x);
>> setPixel(x, 0, v);
>> }
>> makeRectangle(0, 0, 256, 1);
>> run("Copy");
>> for (y=1; y<256; y++) {
>> makeRectangle(0, y, 256, 1);
>> run("Paste");
>> }
>> run("Select None");
>>
>> run("FFT Options...", "fft raw fast complex");
>> run("FD Math...", "image1=test operation=Correlate image2=test
>> result=PowerSpectrum");
>>
>>
>> ________________________________________________________________
>>
>> On 12 Dec 2007, at 23:00, Albert Cardona wrote:
>>
>>> Joachim, Michael,
>>>
>>> Just a note:
>>>
>>> As far as I know, ImageJ's "FFT", which is an FHT as Joachim says,
>>> does not properly replace FFT at all. When trying to rely on it for
>>> Cepstrum
>>> and other uses related to registration we realized how much off
>>> it is
>>> from a proper FFT: a lot.
>>>
>>> We use FFT from jfftw.jar wrapper for native fftw libraries, and in
>>> their absence,
>>> the FFT classes from edu_mines_jtk.jar . Using these, results are
>>> as analitically
>>> expected.
>>>
>>> There are a few example of its uses in the mpi.fruitfly package of
>>> TrakEM2,
>>> implemented by Stephan Preibisch.
>>>
>>> The git repos:
>>>
http://repo.or.cz/w/trakem2.git>>>
>>> The archived source classes:
>>>
http://www.ini.uzh.ch/~acardona/piper.php?file=jars/TrakEM2-
>>> src.zip
>>>
>>> Albert
>>>
>>> --
>>> Albert Cardona
>>>
http://www.mcdb.ucla.edu/Research/Hartenstein/acardona>>
>>
>>
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>>
>
> Robert Dougherty, Ph.D.
> President, OptiNav, Inc.
> 10900 NE 8th St, Suite 900
> Bellevue, WA 98004
> Tel. (425)990-5912
> FAX (425)467-1119
> www.optinav.com
>
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